If I remember correctly from my reading, most of Padre Island is fairly hard packed sand. So it would be a TC's dream.
With your truck being a 3/4 ton, I believe you will find you have 8 ply tires, also known as E rated.
As an off roader, it was common to air down my tires to 15psi for traction. When I first asked about air down the truck tires for carrying the tc on the soft beach of NC, I was told down to about 20 pounds. I couldn't believe being over 10,000 pounds the tires would handle it. So I air down in the driveway and sure enough, was confident there wouldn't be a problem, though think 30psi will be the first attempt until I felt the truck struggling (and hope it isn't too late). Just make sure you have a way to air them back up before you hit the pavement.
Another advantage of airing down is it lets the tires absorb more of the shock from road deviations. In regards to deviation, when going over rocks, if you can't completely avoid the rock, catch the rock completely with the tire. The side walls of the tire is the weak link and easy split by a sharp rock edge.
For a typical non-basement camper, draw a line from the inside edge of the tire to the middle of the top of the truck cab. For a basement camper, I would use the center of the cabover for the top point. This is a good rough line you can make go vertical safely without the truck rolling over based on nothing on the roof. The trick is that the closer you get to that tipping point, the slower you need to go. It is usually the rocking momentum that will do you in.
If you look at Jefe's photo, assuming the camera is level, you will see he still has a good way to go.
